IF AND ONLY IF
SI Y SÓLO SI
Pithagoras
1 Corinthians 15:57
“But thanks be to God, which giveth us the victory through our Lord Jesus Christ.”
What you may have noticed in this and previous chapters is in translating from English to symbolic form we often make use of our background knowledge of what is equivalent to what. That is what happens when we translate "She is here" as S but also "She's here" as S even though the two sentences have different letters; one has an apostrophe, and the other does not. When we translate conditions, we make considerable use of our background knowledge about equivalence. We make use of our knowledge that tense (past, present, future) and mood (indicative, subjunctive) is or is not important for the argument. For example, notice the subtle move from present tense to future tense in this valid argument:
If Samantha takes a car, she'll get there faster.
She will take a car.
So, she will get there faster.
"She takes" is present tensed, but "She will take" is past tensed. We ignore all this tense information when we translate the argument as
If TAKES, then FASTER.
TAKES.
So, FASTER.
It takes a good understanding of the language to know when you can ignore time information and when you cannot. You cannot ignore it in this argument:
If she takes a car, she'll get there faster, but not if she waits another five minutes.
She will take a car, but not for ten minutes.
So, she will get there faster.
No, she won't. This is invalid reasoning.
Here is another example of making use of background information. Is this argument valid?
If Samantha takes a care, she'll get there faster.
She will take a car.
So, she will get there faster.
Maybe. We said it was valid a couple of paragraphs ago, but it is valid only if we are justified in ignoring the fact that the word "she" might be referring to Abraham Lincoln's wife, and not to Samantha. Our background knowledge tells us whether we need to pay attention to this possibility or not.
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